Spectral analysis of numerical solutions to the Burgers–Korteweg–DeVries equation

Finite amplitude acoustic wave propagation through bubbly liquids is studied by using the Burgers–Korteweg–DeVries model equation. Numerical solutions are obtained using a pseudospectral method. Spectral analysis of the numerical solutions is performed to study the spectral energy transfer due to nonlinearity. Numerical solutions of the two limiting cases obtained by neglecting either the dissipation or dispersion term of the Burgers–Korteweg–DeVries equation are also analyzed. In nonlinear wave propagation, short waves are generated by long waves due to nonlinearity. In bubbly media, these short waves may undergo strong resonance absorption due to the presence of bubbles, even if other mechanisms of dissipation are negligible. The effect of such an absorption is simulated by applying a low‐pass filter on the results obtained with the dissipation term neglected. The filter eliminates the short waves generated after each time step. It is shown that such resonance absorption corrections may be necessary for any quantitative comparisons of computed results with experiment.